Association of Selected State Policies and Requirements for Buprenorphine Treatment With Per Capita Months of Treatment

Key Points Question What is the association between selected state policies and buprenorphine dispensing? Findings In this cross-sectional study using US county-level pharmacy claims data, educational requirements for buprenorphine prescribers beyond those required to obtain a waiver were associated with increased buprenorphine dispensing, as was continuing medical education related to substance misuse and addiction. Prescription drug monitoring programs, pain management clinic laws, and Medicaid policies had no association with buprenorphine dispensing. Meaning These findings suggest that meaningful changes in access to buprenorphine may be achieved through greater attention to professional education and clinician knowledge.

Our general approach was to begin by specifying a full set of monthly event-time indicators, starting at the beginning of the study period and placing no limits on time-until policy adoption, and carrying through the end of the study period with no limits on time-since policy adoption. This allowed us to examine evidence of pre-policy adoption trends in event-time with limited restrictions. Following Goodman-Bacon and Borusyak, 1,2 we restricted several arbitrarily-selected pre-policy adoption eventtime indicators to zero to identify event-time policy effects separately from calendar time effects. Without the restrictions, the two time-metrics would only be identified up to a linear trend, which could be generated by either metric. After rejecting long-term trends, we focused on the year before implementation. We set all event-time indicators prior to the 12 th pre-implementation month to zero, and we further scrutinized the period 12-months before policy implementation, the period most likely to show evidence of anticipatory effects should they arise. If we found evidence of anticipatory effects for a policy, we retained that policy's even-time indicators for the 12-month before policy implementation. If we found no evidence of anticipation, we further restricted the last event-time month prior to policy implementation to zero, and we retained the remaining 11 pre-implementation event-time indicators to show the pre-implementation trends. Appendix Table 2 provides our regression results including the year prior to policy implementation, illustrating the anticipatory effects we identified.  We start here by describing a single policy model and then generalizing to the multiple policy model we estimated.

Model with 1 policy.
Let t be a calendar time index and ET be an event time index defined as t less the month of policy implementation. With data structured so that the county-month was the unit of analysis, we express the single policy model as: where is total monthly number in treatment per capita for which i, s, and t index county, state, and calendar month; X is a vector of covariates, is a calendar month indicator for month t, G is a treatment group indicator for all states that ever implemented the policy; , is an indicator for eventtime in state s at time t ( , ); is a vector of state fixed effects; and is an error term. 2 and 3 are parameter vectors for all t, and 4 is a parameter vector for all , and therefore identifies policy associations both before and after policy implementation.
Identification of ET effects: In these models, even with rich data, ET is identified separately from * only up to a common linear trend. Our general approach followed the suggestions of Goodman-Bacon (2021) and Borusyak and colleagues (2022). 1,2 First, we estimated the model with no restrictions on ET and examined the pattern of coefficients. Second, we restricted a set of arbitrarily chosen coefficients of ET<0 (we selected ET=-25, ET=-31, ET=-37, …) to be zero, which required any linear trend to be absorbed by calendar time. In the absence of evidence of long-term pre-implementation trends, we further restricted all ET<-12 to zero and scrutinized the last 12 months before policy implementation.

Considerations
Potential bias in long-duration effects: Variation in the timing of policy implementation across states requires that the horizon with which effects are identified will vary by state. Thus, while it is necessary to admit long-duration effects to ensure that bias is not introduced among other model parameters, their estimates may not be reliable as the number of states supporting them decline. Therefore, although we specified ET monthly through the end of the study period, we test for effects and display results only through 5 years. 1 Focus on average state effects versus average person effects: These models are almost always estimated at the individual level, producing estimated effects for the average person. The models answer questions like: What did these policies do to the U.S. population? To answer questions such as What was the average (across states) effect of a policy that was implemented in 10 states? the data should be weighted to make the contribution of large and small states the same. Because our unit of analysis is the county-month, we want a county's weight to be proportional to its population within the state-month, but we want every state-month to have equal weight. The straight-forward approach is to create weights as where is the population of county i, state s, at time t; and is the population of state s at time t. The sum of the weights for each state-month is 1, but within states the weights are proportional to the size of the county's population. This also addresses concerns about negative weights in regression estimates of heterogenous policy effects over time since policy implementation. 1,2

Model with K policies
Generalizing to multiple policies from (1) generates a large number of parameters and can only work in applications with very rich data. At a minimum, there must be adequate variation in the adoption of policies across states and over time (illustrated above in the policy wheels in Appendix Figure 1 and Appendix Figure 2, which shows both the policy implementation by state by year, using a modification of the figure in the original manuscript which reviewers suggested we revise, as well as now including an illustration of the treatment trend by state). Consider the direct generalization of (1): where k indexes policies. This model calculates the calendar time effects ( 3 ) for each of the K statepolicy groups (G) conditional on ET estimates that may be active during the pre-or post-adoption periods in other state-policy groups. Identifying these effects requires adequate variation (both across states and over time) in each state-policy group and across policies. If in any month, the states in = are the same as in = , the parameters are not identified separately; however, their combined deviation from the main effects is identified, which is sufficient.
We estimated equation (2) and, using the approach described above for the single policy model, we examined the coefficients of each policy for evidence of anticipation. In this application, we found evidence of anticipatory effects for two policies (additional training and continuing medical education). For the remaining four policies, we further restricted the event-time indicator just prior to policy adoption (ET=-1) to zero.

Limitations
There have been many recent advances in event-study models. Although we rely heavily on Goodman-Bacon and Borusyak, 1,2 we have not attempted to adapt the most recently suggested methods, which were developed for single policy models, for use in a multi-policy application, to which less work has been devoted. We also assume treatment effect dynamics are homogenous across states. That is, they follow the same path over time with respect to the policy's effective date. This may not be the case if, for example, there is learning across states. Our model accommodates differences across states in a policy's substantive detail or implementation that affect the magnitude of the policy's effect, but does not allow for relative differences across states in event-time. See Sun and Abraham (2021) 4 for a more detailed discussion.